If you scroll down through the discussion, the APA staff writer elaborates to say:

"When writing a paragraph, you can alternate between citing an author parenthetically and using the author’s name in the running text. You can also use “he” or “she,” when you know the gender of the author (see SA’s reworded paragraph above). Just be sure that these pronouns have a clear referent. By using these variations, you can avoid redundancy in your writing and still make clear throughout the paragraph that the ideas are those of the original researcher.

To your specific question, the Manual does not specify any number of sentences at which an author’s name must be mentioned. The writer’s goal should be to delineate which are his or her original ideas and which are those of other scholars. For more, see pages 15–16 and pages 170–173 of the Manual."